Lipscomb's universal space is the attractor of an infinite iterated function system

Lipscomb's one-dimensional space on an arbitrary index set is injected into the Tychonoff cube . The image of is shown to be the attractor of an iterated function system indexed by . This system is conjugate, under an injection, with a set of right-shift operators on Baire's space regarded as a code space. This view of extends the fractal nature of initiated in a 1992 joint paper by the author and S. Lipscomb. In addition, we give a new proof that as a subspace of Hilbert's space , the space is complete and hence is closed in .

     

Measuring the effects of knowledge in military campaigns

A particularly difficult problem in command and control is that of identifying the relationship between intelligence, decision and combat outcome. The problem centres on three things: (1) an adequate representation of the situation confronting the commander on the battlefield; (2) an adequate measure of combat outcome; and (3) an appropriate metric linking knowledge of the first to the second. In this paper, we focus on the third of these by developing a measure of the knowledge possessed by the commander at the time he takes his decision and by relating this to combat outcomes. Combat outcomes are represented using traditional attrition-based metrics and the combat situation is simply the size, location and identity of enemy units. Therefore, the possible number of identified enemy units arrayed against the friendly commander constitutes the set of hypotheses on alternative situations. Surveillance assets provide the commander with evidence that is used to update the probability distribution. Knowledge if then represented as the product of two components: residual knowledge, the knowledge gained from the updated probability distribution, and detection knowledge, the knowledge from the detection itself. Information entropy was used to develop a metric that reflects the degree to which the commander understands the situation confronting him. The metric was applied in a UK Ministry of Defence study of a proposed Airborne STand-Off Radar (ASTOR) to measure the effects of improved surveillance on combat outcomes.     

Small cluster models of the surface electronic structure and bonding properties of titanium carbide, vanadium carbide, and titanium nitride

Density functional theory (DFT) calculations on stoichiometric, high-symmetry clusters have been performed to model the (100) and (111) surface electronic structure and bonding properties of titanium carbide (TiC), vanadium carbide (VC), and titanium nitride (TiN). The interactions of ideal surface sites on these clusters with three adsorbates, carbon monoxide, ammonia, and the oxygen atom, have been pursued theoretically to compare with experimental studies. New experimental results using valence band photoemission of the interaction of O(2) with TiC and VC are presented, and comparisons to previously published experimental studies of CO and NH(3) chemistry are provided. In general, we find that the electronic structure of the bare clusters is entirely consistent with published valence band photoemission work and with straightforward molecular orbital theory. Specifically, V(9)C(9) and Ti(9)N(9) clusters used to model the nonpolar (100) surface possess nine electrons in virtually pure metal 3d orbitals, while Ti(9)C(9) has no occupation of similar orbitals. The covalent mixing of the valence bonding levels for both VC and TiC is very high, containing virtually 50% carbon and 50% metal character. As expected, the predicted mixing for the Ti(9)N(9) cluster is somewhat less. The Ti(8)C(8) and Ti(13)C(13) clusters used to model the TiC(111) surface accurately predict the presence of Ti 3d-based surface states in the region of the highest occupied levels. The bonding of the adsorbate species depends critically on the unique electronic structure features present in the three different materials. CO bonds more strongly with the V(9)C(9) and Ti(9)N(9) clusters than with Ti(9)C(9) as the added metal electron density enables an important pi-back-bonding interaction, as has been observed experimentally. NH(3) bonding with Ti(9)N(9) is predicted to be somewhat enhanced relative to VC and TiC due to greater Coulombic interactions on the nitride. Finally, the interaction with oxygen is predicted to be stronger with the carbon atom of Ti(9)C(9) and with the metal atom for both V(9)C(9) and Ti(9)N(9). In sum, these results are consistent with labeling TiC(100) as effectively having a d(0) electron configuration, while VC- and TiN(100) can be considered to be d(1) species to explain surface chemical properties.     

Enhancement of stereospecificity in isoprene polymerization with alkylaluminum–titanium chloride catalysts through use of carbon disulfide

The effect of CS₂ on isoprene polymerization with triisobutylaluminum-titanium tetrachloride catalysts was studied at Al/Ti ratios of optimum (0.9) and higher values. In the absence of CS₂, appreciable amounts of low molecular weight oils (“extractables”) were formed at the expense of cis-1,4-polyisoprene with higher than optimum Al/Ti ratios. Small amounts of CS₂ were found to prevent extractables formation and allow attainment of higher yields of cis-1,4-polyisoprene. The optimum CS₂/Ti chloride molar ratio (0.1) was independent of the Al/Ti ratio of the catalyst. Polymer microstructure and dilute solution viscosity were unaffected by CS₂. The results support the theory that the catalyst surfaces hold two types of active sites: p-sites, which initiate polymerization, and o-sites, which lead to oligomerization. CS₂ appears to enhance polymerization by coordinating selectively at the o-sites. The predominance of oligomerization at the higher Al/Ti ratios was attributed to a destruction of p-sites by excess trialkyl-aluminum.     

Bis-(8-oxo quinoline)diorgano tellurium(IV) compounds; structural and spectroscopic studies

Three new compounds of the type R₂Te(OR′)₂ are reported in which R′ bears a potentially co-ordinating group: bis-(8-hydroxo quinoline)dimethyltellurium (I) bis-(8-oxo-2-methyl quinoline)dimethyltellurium (II), and bis-(8-oxo-quinoline) di-(p-tolyl)tellurium (III). The crystal structures of II and III have been determined. The primary geometry around tellurium in both cases can be described as ψ-trigonal bipyramidal but long Te N contacts in the range 2.840(6)–2.899(4) Å which lie well within the van der Waals distance imply extension of the co-ordination sphere. Variable temperature multi-nuclear (¹ H, ¹³C, ¹²⁵Te) studies of the compounds I, II, and III in solution indicate the presence of a single species over the range 216–343 K. The data do not distinguish between the presence of a single 14-Te-6 pertellurane seen in the crystallographic studies, or that of such a species in equilibrium, rapid on the ¹H and ¹²⁵Te timescales, with the 10-Te-4 tellurane.     

Identification and quantification of eight flavones in root and shoot tissues of the medicinal plant huang-qin (Scutellaria baicalensis Georgi) using high-performance liquid chromatography with diode array and mass spectrometric detection

A method of analysis of eight flavones using high-performance liquid chromatography (HPLC)-diode array detection (DAD)-mass spectrometry (MS) in root and aerial tissues of the medicinal plant Scutellaria baicalensis was developed. The identity of the analytes was confirmed using retention time, UV-vis and mass spectral comparisons to commercial standards. Both UV-vis and mass spectral patterns were characterized for glycosylated flavones. Two additional flavone glycosides were tentatively identified as chrysin-7-glucuronide and wogonoside, but not quantified. Greenhouse and in vitro-grown tissues were analyzed with flavone concentrations ranges of 0.14-150 and 0.030-1.7 microg/mg for greenhouse root and shoot tissue, respectively, and 0.0068-6.4 and 0.082-1.5 microg/mg for in vitro-grown roots and shoots, respectively.     

Platinum-rhodium carbonyl clusters: new structures and new types of dynamical activity

The reaction of Rh(4)(CO)(12) with Pt(PBu(t)(3))(2) in CH(2)Cl(2) at room temperature yielded three new complexes: Rh(4)(CO)(4)-(mu-CO)(4)(mu(4)-CO)(PBu(t)(3))(2)[Pt(PBu(t)(3))], 10, Rh(2)(CO)(8)[Pt(PBu(t)(3))](2)[Pt(CO)], 11, and Rh(2)(CO)(8)[Pt(PBu(t)(3))](3), 12. The reaction of Rh(4)(CO)(12) with an excess of Pt(PBu(t)(3))(2) in hexane at 68 degrees C yielded the new hexarhodium-tetraplatinum compound, Rh(6)(CO)(16)[Pt(PBu(t)(3))](4), 13, in a low yield. All four compounds were characterized by (31)P NMR and single-crystal X-ray diffraction analyses. Compound 10 contains an unsymmetrical quadruply bridging carbonyl ligand in the fold of a butterfly tetrahedral cluster of four rhodium atoms with a Pt(PBu(t)(3)) group bridging the hinge of the butterfly tetrahedron. Compound 11 contains an unsaturated trigonal bipyramidal Rh(2)Pt(3) cluster. Compound 12 is similar to 11 except the trigonal bipyramidal Rh(2)Pt(3) cluster opened by cleavage of one Pt-Rh bond due to steric interactions produced by the replacement of one of the carbonyl ligands in 11 with a tri-tert-butylphosphine ligand. Compound 12 undergoes facile dynamical rearrangements of the metal atoms in the cluster which average the three inequivalent phosphine ligands on the platinum atoms. Compound 13 contains an octahedral cluster of six rhodium atoms with four Pt(PBu(t)(3)) groups bridging edges of that octahedron.